Wiese suffered the injury to his right hand when trying to take a catch off his own bowling during a warm-up match ahead of the season and required surgery which will keep him out for up to six weeks.
Faf du Plessis, the T20 captain, acknowledged Wiese was a significant loss and admitted Morkel has earned a chance he thought may have passed him by.
"David is a fantastic player for us in the T20 format. He has done really well. His bowling is going to be missed the most. He has been a banker from a captain's point of view. You know what you are going to get from him. He is pretty clever in the middle, he is a very smart bowler.
"Albie brings a lot of experience. I suppose Albie would have thought his time is up, once again, but he is getting another opportunity because he is a quality player. For him, its important to try and also put a stake, even if he wasn't in our thinking and our plans, he is getting an opportunity to make it so."
Meanwhile, Rilee Rossouw has been ruled out of the entire limited-overs leg of the India tour as he continues his recovery from a stress fracture to his foot he sustained against New Zealand with the South Africa medical team being careful not to rush him back.
Rossouw was not set to play the T20s, but had been in line for the one-day series which followed. His place will be taken by uncapped batsman Khaya Zondo who was already part of the T20 squad.
"The medical committee have decided its still too early for him to be pushed at this stage," South Africa team manager Mohammed Moosajee said. "The plan is to get him to be ready by the end of October."
There was better news regarding du Plessis with his knee injury, which kept him out of the New Zealand limited-overs matches in August, having recovered significantly although he will be watched closely in India, especially as he is one of only six players included in all three formats. "I was batting in the nets this week with Gary [Kirsten] and I feel good," he said.
To complete a lengthy fitness bulletin ahead of the team's departure to India, Chris Morris was given the all-clear after coming through three T20 warm-up matches for his franchise, the Titans, having recovered from the groin strain which hampered him in Bangladesh.